Singularity Formation in Systems of Non-strictly
Hyperbolic Equations

R. Saxton & V. Vinod

Abstract:
We analyze finite time singularity formation for two systems
of hyperbolic equations. Our results extend previous proofs of breakdown
concerning
non-strictly hyperbolic systems to
systems, and to a situation where, additionally, the condition of
genuine nonlinearity is violated throughout phase space. The systems
we consider include as special cases those examined by Keyfitz and
Kranzer and by Serre. They take the form
where
is a scalar-valued function of the n-dimensional
vector
, and
under the assumption
with
,
where
.